Is there a way to calculate the number of solutions to $n$ by $n$ queen problem(done by backtracking) or it's complex and already defined as in the following table
2026-05-04 22:44:23.1777934663
How many solutions are there to an $n$ by $n$ queens problem?
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As pointed out in a comment, if you already know this many terms of a sequence, you can usually find most of what's known about it at OEIS.
The number of solutions is OEIS sequence A000170.
The number of equivalence classes of solutions under isometries is OEIS sequence A002562.
Neither entry provides a closed form, recurrence or generating function.